Effective Wess-Zumino-Witten Action for Edge States of Quantum Hall Systems on Bergman Ball

Abstract

Using a group theory approach, we investigate the basic features of the Landau problem on the Bergman ball {\bf B}^k. This can be done by considering a system of particles living on {\bf B}^k in the presence of an uniform magnetic field B and realizing the ball as the coset space SU(k,1)/U(k). In quantizing the theory on {\bf{B}}^k, we define the wavefunctions as the Wigner \cal{D}-functions satisfying a set of suitable constraints. The corresponding Hamiltonian is mapped in terms of the right translation generators. In the lowest Landau level, we obtain the wavefunctions as the SU(k,1) coherent states. This are used to define the star product, density matrix and excitation potential in higher dimensions. With these ingredients, we construct a generalized effective Wess-Zumino-Witten action for the edge states and discuss their nature.

arXiv comment19 pages, clarifications and some equations removed, version published in NPB

References in corpus (21)

• A Four Dimensional Generalization of the Quantum Hall Effect
• Quantum Hall Effect in Higher Dimensions
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• The Eight Dimensional Quantum Hall Effect and the Octonions
• The effective action for edge states in higher dimensional quantum Hall systems
• One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory
• Higher-Dimensional Quantum Hall Effect in String Theory
• Edge States for quantum Hall droplets in higher dimensions and a generalized WZW model
• The Spectrum of the Dirac Operator on Coset Spaces with Homogeneous Gauge Fields
• Collective excitations at the boundary of a 4D quantum Hall droplet
• Non-commutative geometry of 4-dimensional quantum Hall droplet
• Dimensional Hierarchy in Quantum Hall Effects on Fuzzy Spheres
• Chiral actions from phase space (quantum Hall) droplets
• Quantum Hall Effect on Higher Dimensional Spaces
• Geometric construction of the Quantum Hall Effect in all even dimensions
• W_{\infty} Gauge Transformations and the Electromagnetic Interactions of Electrons in the Lowest Landau Level
• Finding the remnants of lost jets at RHIC
• Kac-Moody theories for colored phase space (quantum Hall) droplets
• Collective Variables of Fermions and Bosonization
• Oscillator potential for the four-dimensional Hall effect
• Metallic Nature of the Four-Dimensional Quantum Hall Edge

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• Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect
• Symmetries of N=4 supersymmetric CP(n) mechanics
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• 5d-4d Correspondence in Twisted M-theory on a Conifold
• Electromagnetic Excitations of A_n Quantum Hall Droplets
• Noncommutative scalar fields from symplectic deformation
• Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space